"Once we got the physical squared away, there was no question he was going to become a Giant," said general manager Brian Sabean, who credited the pitcher for his swift decision.
Hudson made his major league debut with the Athletics in 1999 and went 92-39 in six seasons with Oakland, where the right-hander teamed with Mark Mulder and Barry Zito to form a successful "Big Three."
The 38-year-old went 8-7 with a 3.97 ERA in 21 starts this season for Atlanta. His season was cut short by a broken right ankle that required surgery. The Braves earlier this month declined to make a qualifying offer to Hudson, who won 49 games during the previous three seasons.
Hudson was hurt July 24 in New York when the Mets' Eric Young Jr. inadvertently stepped on the back of the pitcher's lower right leg while Hudson covered first base.
While he hasn't begun running on the ankle yet, he had a screw removed last week and expects to be full strength for spring training.